Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<cstdio>
#define SF scanf
#define PF printf
#define MAXN 200010
using namespace std;
int n;
int p[MAXN],q[MAXN],ans[MAXN],f[MAXN];
bool ord(int x,int y,int z){
	if(x<y&&y<z)
		return 1;
	if(y<z&&z<x)
		return 1;
	if(z<x&&x<y)
		return 1;
	return 0;	
}
int main(){
	SF("%d",&n);	
	for(int i=1;i<=n;i++){
		SF("%d",&p[i]);
		q[p[i]]=i;
	}
	for(int i=n-1;i>=1;i--){
		if(ans[i+1]==0){
			if(q[i]>q[i+1]){
				ans[i]=1;
				f[i]=i+1;
			}
		}
		else{
			if(ord(q[i],q[i+1],q[f[i+1]])){
				ans[i]=ans[i+1];
				f[i]=f[i+1];
			}
			else{
				ans[i]=ans[i+1]+1;
				f[i]=i+1;	
			}
		}
	}
	PF("%d",ans[1]);
}